LECTURE 25 MAGNETISM & MAGNETIC FORCE ON CHARGED PARTICLES

Instructor: Kazumi Tolich

Lecture 25 2

! Reading chapter 22-1 to 22-3 ! Magnetic fields and force ! Motion of a point charge in a B field

" Cyclotron motion " Velocity selector "q/m measurement for electrons " Mass spectrometer " Cyclotron

Magnetic poles

! Magnets have two magnetic poles: a north pole and a south pole.

! North and south poles always come in pairs. We have not seen a magnetic monopole, a north or south pole by itself.

! On Valentines day, 1982, there was one candidate monopole observed, but this has never been reproduced.

Phys. Rev. Lett. 48 1378

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Magnetic force 4

! Like poles repel, and unlike poles attract.

! This is not the electric force, and the ends of the magnet are not electrically charged.

! This force is the magnetic force.

! If a magnet is broken in half, each half has two poles:

Demo: 1 5

! Magnets on turntable ! Demonstration of magnetic attraction and repulsion

Magnetic fields

! Magnetic field is the thing that transmits the magnetic force.

! A magnetic field surrounds every moving charged object.

! The existence of a magnetic field means that if an appropriate moving charged object is nearby, it will experience a force.

! An magnetic field is the possibility of a magnetic force.

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Magnetic field lines 7

! Magnetic fields are visualized by magnetic field lines.

! Magnetic field lines always make complete loops. They neither begin nor end.

! Field lines never cross.

! By definition, magnetic field lines exit from the north pole of a magnet and enter at the south pole.

Magnetic field lines: 2 8

! The density of field lines indicate the magnitude of the field.

! Iron filings sprinkled around a bar magnet align themselves with the magnetic field.

Force by a magnetic field 9

! The magnitude of magnetic force on a moving charged particle is given by

is the angle between the magnetic field and the velocity of the charged particle.

! This is an experimental result we observe it to be true. It is not a consequence of anything weve learned so far.

F = q vBsin

Definition of magnetic field 10

! The magnetic force on a moving charge is actually used to define the magnetic field:

! The unit of magnet field, B, is called the tesla, T, which is equivalent to N/(A#m).

! Another common unit of magnetic field is the gauss, G.

B = Fq vsin

1 T = 104 G

Magnetic force vector 11

! In order to figure out which direction the force is on a moving charge, you can use a right-hand rule.

! This gives the direction of the force on a positive charge; the force on a negative charge would be in the opposite direction.

! The vector form of magnetic force is given by

!F = q!v !B

Work done by a magnetic field 12

! The direction of the magnetic force is always perpendicular to both velocity and the B field.

! Magnetic forces on point charges do no work.

Example: 1 13

! An alpha particle (charge q=3.210-19C and mass m=6.610-27kg) travels at a velocity, v, of magnitude 550m/s through a uniform magnetic field, B, of magnitude 0.045T. The angle between v and B is =52. What are the magnitudes of a) the force acting on the particle due to

the magnetic field?

b) the acceleration of the particle due to the force?

c) Does the speed of the particle change?

Motions in E vs. B 14

! A positively charged particle in an electric field experiences a force in the direction of the field.

! In a magnetic field the force is perpendicular to the field. This leads to very different motions:

The velocity selector 15

! If a particle is moving in perpendicular E and B fields, it gets deflected unless its velocity (v=E/B) results in balancing the electric and magnetic forces.

Demo: 2 16

! Magnetic deflection ! Demonstration of an electron beam deflected by the

magnetic field from a bar magnet

!F = q!v !B

Circular motion in magnetic fields 17

! The magnetic force is always perpendicular to the velocity, therefore the particle undergoes uniform circular motion.

! If the magnetic field is also perpendicular to the velocity then for a particle of mass m and charge q, moving at a speed v in a magnetic field B, the radius of the circle it travels is:

r = mvq B! The period to complete a circle T is

independent of v or r and given by

T = 2mqB

Demo: 3 18

! Fine beam tube ! Demonstration of an electron beam bent into a circle by

magnetic field

r = mvq B

The mass spectrometer 19

! The mass spectrometer measures masses of isotopes.

! Positive ions are accelerated through potential difference, V.

! Ions enter the B field, and get deflected.

mq =

B2r22V

Particle identification 20

Bubbles form around the paths of particles in a bubble chamber. The curvature depends on the momentum and the charge of the particle.

r = mvq B

Helical motion 21

! If the magnetic field is not perpendicular to the velocity, the component of velocity parallel to the B field does not change since there is no magnetic force along that direction.

! The particle moves in a helical path.

The helical path of an electron in a cloud chamber.

Magnetic bottle 22

! Magnetic field is stronger on both ends than in the middle.

! The particle spirals around the field lines and oscillates back and forth.

What causes aurora?

! Charged particles ejected from the sun are trapped by Earths magnetic field, entering Earths atmosphere at the north and south magnetic poles.

! The charged particles interact with the gas in the area to produce light.

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Neutrino mass measurement 24

Thomsons q/m measurement 25

! J. J. Thomson discovered electrons and measured the q/m ratio of electrons by shooting electrons in E and B fields.

! By tuning the B field, velocity of electrons were measured using the principle of velocity selector.

! With the B field off, the amount of deflection depends on a=qE/m.

Clicker question: 1 26

The cyclotron 27

! Cyclotrons were invented to accelerate particles for studies of nuclei.

LHC (Large Hadron Collider) 28

! LHC is the largest particle accelerator, synchrotron (27km circumference).

! It speeds up and increases the energy of a beam of particles by generating electric fields that accelerate the particles, and magnetic fields that steer and focus them.